This paper characterizes those pseudo-Anosov mappings whose entropy can be detected homologically by taking a limit over finite covers. The proof is via complex-analytic methods. The same methods show the natural map , which sends a Riemann surface to the Jacobians of all of its finite covers, is a contraction in most directions.
Cite this article
Curtis T. McMullen, Entropy on Riemann surfaces and the Jacobians of finite covers. Comment. Math. Helv. 88 (2013), no. 4, pp. 953–964DOI 10.4171/CMH/308